The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.

collective noun

NOUN: A noun that denotes a collection of persons or things regarded as a unit.

USAGE NOTE: In American usage, a collective noun takes a singular verb when it refers to the collection considered as a whole, as in The family was united on this question. The enemy is suing for peace. It takes a plural verb when it refers to the members of the group considered as individuals, as in My family are always fighting among themselves. The enemy were showing up in groups of three or four to turn in their weapons. In British usage, however, collective nouns are more often treated as plurals: The government have not announced a new policy. The team are playing in the test matches next week. A collective noun should not be treated as both singular and plural in the same construction; thus The family is determined to press its (not their) claim. Among the common collective nouns are committee, clergy, company, enemy, group, family, flock, public, and team. See Usage Notes at government, group.

Many refers to an indefinite number, while much refers to an indefinite quantity:

many . . . ADJECTIVE: Inflected forms: more, most 1. Being one of a large indefinite number; numerous: many a child; many another day. 2. Amounting to or consisting of a large indefinite number: many friends.

NOUN: (used with a pl. verb) 1. A large indefinite number: A good many of the workers had the flu. 2. The majority of the people; the masses: “The many fail, the one succeeds” (Tennyson).

PRONOUN: (used with a pl. verb) A large number of persons or things: “For many are called, but few are chosen” (Matthew 22:14).

IDIOM: as many The same number of: moved three times in as many years.

ETYMOLOGY: Middle English, from Old English manig. See menegh- in Appendix I.

Well, yes, and no; you just had to pick that word, didn't you? Check the definition and usage of people. In part, the Usage Note says:

. . . Some grammarians have insisted that people is a collective noun that should not be used as a substitute for persons when referring to a specific number of individuals. By this thinking, it is correct to say Six persons were arrested, not Six people were arrested. But people has always been used in such contexts, and almost no one makes the distinction anymore. . . .

The most common usage is "how many people".

So, what makes the difference here?

Again, it's indefinite number versus indefinite quantity. See the first definition in the link above:

1. Humans considered as a group or in indefinite numbers: People were dancing in the street. I met all sorts of people.

To put it another way, individuals or discrete "things" are measured in numbers (how many?), "stuff" is measured in quantity (how much?).

How much sugar? (What quantity of sugar?)Two cups of sugar.

How many cups of sugar? (How many units of measure of sugar?)Two cups.

How many nails? (How many individual nails?)A dozen.or [if you need a lot more. ]Two pounds. (How manyunits of measure of nails?)

Regards//Larry

"To preserve liberty, it is essential that the whole body of the people always possess arms, and be taught alike, especially when young, how to use them." -- Attributed to Richard Henry Lee